C H A P T E R 14
Waves
Chapter Preview
1
Types of Waves
What Is a Wave?
Vibrations and Waves
Transverse and Longitudinal Waves
2
Characteristics of Waves
Wave Properties
Wave Speed
The Doppler Effect
3
Wave Interactions
Reflection, Diffraction, and Refraction
Interference
Standing Waves
452
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Focus
ACTIVITY
Background The energy in an ocean wave can lift a surfboard
up into the air and carry the surfer into shore. Ocean waves get
most of their energy from the wind. A wave may start as a small
ripple in a calm sea, then build up as the wind pushes it along.
Waves that start on the coast of northern Canada may be very
large by the time they reach a beach in the Hawaiian Islands.
The winds that create ocean waves are caused by convection
currents in the atmosphere, which are driven by energy from the
sun. Energy travels across empty space from the sun to Earth—
in the form of light waves.
Waves are all around us. As you read this book, you are depending on light waves. Light bounces off the pages and into your
eyes. When you talk with a friend you are depending on sound
waves traveling through the air. Sometimes the waves can be gentle, such as those that rock a canoe in a pond. Other times waves
can be very destructive, such as those created by earthquakes.
Activity 1 Fill a long, rectangular pan with water. Experiment
with making waves in different ways. Try making waves by sticking the end of a pencil into the water, by moving a wide stick or
board back and forth, and by striking the side of the pan. Place
wooden blocks or other obstacles into the pan, and watch how
the waves change when they encounter the obstacles.
Activity 2 With some of your classmates, practice the “wave”
as is often performed by fans at football games. How does it
resemble an ocean wave? How does it differ from other forms
of motion?
www.scilinks.org
Topic: Waves SciLinks code: HK4150
A surfer takes advantage
of the energy in ocean
waves. Energy travels
from the sun to Earth
in the form of waves.
Pre-Reading Questions
1. What things do you do every day that
2.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
depend on waves? What kinds of waves
do you think are involved?
What properties do you think these different kinds of waves have in common?
453
SECTION
1
Types of Waves
▲
OBJECTIVES
KEY TERMS
wave
medium
mechanical wave
electromagnetic wave
transverse wave
longitudinal wave
>
>
Recognize that waves transfer energy.
>
Explain the relationship between particle vibration
>
and wave motion.
Distinguish between transverse waves and
longitudinal waves.
Distinguish between mechanical waves and
electromagnetic waves.
W
hen a stone is thrown into a pond, it creates ripples on the
surface of the water, as shown in Figure 1. If there is a leaf
floating on the water, the leaf will bob up and down and back and
forth as each ripple, or wave, disturbs it. But after the waves pass,
the leaf will almost return to its original position on the water.
What Is a Wave?
▲
wave a periodic disturbance
in a solid, liquid, or gas as
energy is transmitted through
a medium
Like the leaf, individual drops of water do not travel outward
with a wave. They move only slightly from their resting place as
each ripple passes by. If drops of water do not move very far as a
wave passes, and neither does a leaf on the surface of the water,
then what moves along with the wave? Energy does. A wave is not
just the movement of matter from one place to another. A wave
is a disturbance that carries energy through matter or space.
Figure 1
A stone thrown into a pond
creates waves.
454
C H A P T E R
1 4
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Most waves travel through a medium
The waves in a pond are disturbances traveling
through water. Sound also travels as a wave. The
sound from a stereo is a pattern of changes in
the air between the stereo speakers and your
ears. Earthquakes create waves, called seismic
waves, that travel through Earth.
In each of these examples, the waves involve
the movement of some kind of matter. The matter through which a wave travels is called the
medium. In the example of the pond, the water
is the medium. For sound from a stereo, air is
the medium. And in earthquakes, Earth itself is
the medium.
Waves that require a medium are called
mechanical waves. Almost all waves are mechanical waves, with one important exception:
light waves.
Light does not require a medium
Connection to
ENGINEERING
I
f you have ever been hit by an ocean wave at
the beach, you know these waves carry a lot
of energy. Could this energy be put to good use?
Research is currently underway to find ways
to harness the energy of ocean waves. Some
small floating navigation buoys, which shine
lights to help ships find their way in the dark,
obtain energy solely from the waves. A few larger
systems are in place that harness wave energy to
provide electricity for small coastal communities.
Making the Connection
1. In a library or on the Internet, research different types of devices that harness wave
energy. How much power do some of these
devices provide? Is that a lot of power?
2. Design a device of your own to capture the
energy from ocean waves. The device should
take the motion of waves and convert it into
a motion that could be used to drive a
machine, such as a pump or a wheel.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
mechanical wave a wave
that requires a medium
through which to travel
▲
Energy is the ability to exert a force over a certain distance. It is
also known as the ability to do work. We know that waves carry
energy because they can do work. For example, water waves can
do work on a leaf, on a boat, or on a beach. Sound waves can do
work on your eardrum. Light waves can do work on your eye or
on photographic film.
A wave caused by dropping a stone in a pond might carry
enough energy to move a leaf up and down several centimeters.
The bigger the wave is, the more energy it carries. A cruise ship
moving through water in the ocean could create waves big
enough to move a fishing boat up and down a few meters.
medium a physical environment in which phenomena
occur
▲
Waves transfer energy
▲
Light can travel from the sun to Earth across the
empty space between them. This is possible
because light waves do not need a medium
through which to travel. Instead, light waves
consist of changing electric and magnetic fields in space. For that
reason, light waves are also called electromagnetic waves.
Visible light waves are just one example of a wide range of
electromagnetic waves. Radio waves, such as those that carry signals to your radio or television, are also electromagnetic waves.
Other kinds of electromagnetic waves will be introduced in
Section 2. In this book, the terms light and light wave may refer
to any electromagnetic wave, not just visible light.
electromagnetic wave a
wave that consists of oscillating electric and magnetic
fields, which radiate outward
at the speed of light
WAVES
455
Figure 2
This portrait of a tsunami was
created by the Japanese artist
Hokusai in 1830.
Figure 2 shows a woodblock print of a tsunami, a huge ocean
wave caused by earthquakes. A tsunami may be as high as 30 m
when it reaches shore, taller than a 10-story building. Such waves
carry enough energy to cause a lot of damage to coastal towns
and shorelines. Normal-sized ocean waves do work on the shore,
too, breaking up rocks into tiny pieces to form sandy beaches.
Energy may spread out as a wave travels
Figure 3
Sound waves from a stereo
speaker spread out in spherical
wave fronts.
456
C H A P T E R
1 4
If you stand next to the speakers at a rock concert, the sound
waves may damage your ears. Likewise, if you look at a bright
light bulb from too close, the light may damage your eyes. But if
you are 100 m away, the sound of the rock band or the light from
the bulb is harmless. Why?
Think about waves created when a stone falls into a pond.
The waves spread out in circles that get bigger as the waves move
farther from the center. Each of these circles, called a wave front,
has the same amount of total energy. But as the circles get larger,
the energy spreads out over a larger area.
When sound waves travel in air, the waves spread out in
spheres, as shown in Figure 3. These spheres are similar to the
circular ripples on a pond. As they travel outward, the spherical
wave fronts get bigger, so the energy in the waves spreads out
over a larger area. This is why large amplifiers and speakers are
needed to fill a concert hall with sound, even though the same
music can sound just as loud if it is played on a portable radio
and listened to with a small pair of headphones.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Vibrations and Waves
When a singer sings a note, vocal cords in the singer’s throat
move back and forth. That motion makes the air in the throat
vibrate, creating sound waves that eventually reach your ears.
The vibration of the air in your ears causes your eardrums to
vibrate. The motion of the eardrum triggers a series of electrical
pulses to your brain, and your brain interprets them as sounds.
Waves are related to vibrations. Most waves are caused by a
vibrating object. Electromagnetic waves may be caused by
vibrating charged particles. In a mechanical wave, the particles
in the medium also vibrate as the wave passes through the
medium.
www.scilinks.org
Topic: Vibrations and
Waves
SciLinks code: HK4145
Vibrations involve transformations of energy
Figure 4 shows a mass hanging on a spring. If the mass is pulled
down slightly and released, it will begin to move up and down
around its original resting position. This vibration involves transformations of energy, much like those in a swinging pendulum.
When the mass is pulled away from its resting place, the
mass-spring system gains elastic potential energy. The spring
exerts a force that pulls the mass back to its original position.
As the spring moves back toward the original position, the
potential energy in the system changes to kinetic energy. The
mass moves beyond its original resting position to the other side.
At the top of its motion, the mass has lost all its kinetic
energy. But the system now has both elastic potential energy and
gravitational potential energy. The mass moves downward again,
past the resting position, and back to the beginning of the cycle.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Figure 4
When a mass hanging on a spring
is disturbed from rest, it starts to
vibrate up and down around its
original position.
WAVES
457
Science
and the Consumer
Shock Absorbers:
Why Are They Important?
umps in the road are certainly a nuisance, but
without strategic use of damping devices, they
could also be very dangerous. To control a car
going 100 km/h (60 mi/h), a driver needs all the
wheels of the vehicle on the ground. Bumps in the road
lift the wheels off the ground and may rob the driver of
control of the car.
B
Shock absorber
Coil spring
Shock Absorbers Dampen Vibrations
Modern automobiles are fitted with devices known
as shock absorbers that absorb energy without prolonging vibrations. Shock absorbers are fluid-filled
tubes that turn the simple harmonic motion of the
springs into a damped harmonic motion. In a
damped harmonic motion, each cycle of stretch and
compression of the spring is much smaller than the
previous cycle. Modern auto suspensions are set up
so that all a spring’s energy is absorbed by the shock
absorbers in just one up-and-down cycle.
Shock Absorbers and Springs Come
in Different Arrangements
Shock absorber Leaf spring
Springs Absorb Energy
To solve this problem, cars are fitted with springs at
each wheel. When the wheel of a car goes over a
bump, the spring absorbs kinetic energy so that the
energy is not transferred to the rest of the car. The
energy becomes elastic potential energy in the spring,
which then allows the spring to push the wheel back
down onto the road.
Different types of springs and shock absorbers are
combined to give a wide variety of responses. For
example, many passenger cars have coil springs
with shock absorbers parallel to the springs, or even
inside the springs, as shown at near left. Some larger
vehicles have heavy-duty leaf springs made of stacks
of steel strips. Leaf springs are stiffer than coil
springs, but they can bear heavier loads. In this type
of suspension system, the shock absorber is perpendicular to the spring, as shown at far left.
The stiffness of the spring can affect steering
response time, traction, and the general feel of the
car. Because of the variety of combinations, your
driving experiences can range from the luxurious
“floating-on-air” ride of a limousine to the bonerattling feel of a true sports car.
Springs Alone Prolong Vibrations
Once a spring is set in motion, it tends to continue
vibrating up and down in simple harmonic motion.
This can create an uncomfortable ride, and it may
also affect the driver’s control of the car. One way
to cut down on unwanted vibrations is to use stiff
springs that compress only a few centimeters with
thousands of newtons of force. However, the stiffer
the spring is, the rougher the ride is and the more
likely the wheels are to come off the road.
458
C H A P T E R
1 4
Your Choice
1. Making Decisions If you were going to haul
heavy loads, would you look for a vehicle with
coil springs or leaf springs? Why?
2. Critical Thinking How do shock absorbers
stop an automobile from continually bouncing?
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Figure 5
Whenever the spring is expanded or compressed, it is exerting a force that pushes the mass back almost to the original resting position. As a result, the mass will continue to bounce up and
down. This type of vibration is called simple harmonic motion.
A wave can pass through a series
of masses on springs. The masses
act like the particles in a medium.
A wave can pass through a series of vibrating objects
Imagine a series of masses and springs tied together in a row, as
shown in Figure 5. If you pull down on a mass at the end of the
row, that mass will begin to vibrate up and down. As the mass on
the end moves, it pulls on the mass next to it, causing that mass
to vibrate. The energy in the vibration of the first mass, which is
a combination of kinetic energy and elastic potential energy, is
transferred to the mass-spring system next to it. In this way, the
disturbance that started with the first mass travels down the row.
This disturbance is a wave that carries energy from one end of
the row to the other.
If the first mass were not connected to the other masses, it
would keep vibrating up and down on its own. However, because
it transfers its energy to the second mass, it slows down and then
returns to its resting position. A vibration that fades out as
energy is transferred from one object to another is called damped
harmonic motion.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
WAVES
459
How do particles move in a medium?
Materials
✔ long, flexible spring
✔ colored ribbon
1. Have two people each grab an end of the spring
and stretch it out along a smooth floor. Have
another person tie a small piece of colored ribbon to a coil near the middle of the spring.
2. Swing one end of the spring from side to side.
This will start a wave traveling along the spring.
Observe the motion of the ribbon as the wave
passes by.
3. Take a section of the spring and bunch it
together as shown in the figure at right. Release
the spring. This will create a different kind of
wave traveling along the spring. Observe the
motion of the ribbon as this wave passes by.
Analysis
1. How would you describe the motion of the
ribbon in step 2? How would you describe its
motion in step 3?
2. How can you tell that energy is passing along
the spring? Where does that energy come from?
The motion of particles in a medium is like the motion of
masses on springs
If you tie one end of a rope to a doorknob, pull it straight, and
then rapidly move your hand up and down once, you will generate a single wave along the rope, as shown in Figure 6. A small
ribbon tied to the middle of the rope can help you visualize the
motion of a single particle of matter in the rope.
As the wave approaches, the ribbon moves up in the air, away
Figure 6
from its resting position. As the wave passes farther along the
As this wave passes along a rope,
rope, the ribbon drops below its resting position. Finally, after
the ribbon moves up and down
the wave passes by, the ribbon returns to its original starting
while the wave moves to the right.
point. Like the ribbon, each
part of the rope moves up and
down as the wave passes by.
The motion of each part
of the rope is like the vibrating motion of a mass hanging on a spring. As one part
Particle
motion
of the rope moves, it pulls on
the part next to it, transferring energy. In this way, a
wave passes along the length
Wave motion
of the rope.
460
C H A P T E R
1 4
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Quick
Transverse and Longitudinal Waves
Particles in a medium can vibrate either up and down or back
and forth. Waves are often classified by the direction that the particles in the medium move as a wave passes by.
Quick
Quick
Polarization
Polarizing filters block all light
except those waves that oscillate in a certain direction.
Look through two polarizing
filters at once. Then rotate
one by 90° and look again.
What do you observe?
Transverse waves have perpendicular motion
Suppose you stretch out a long, flexible spring on a table or a
smooth floor, grab one end, and move your hand back and forth,
directly toward and directly away from the other end of the
spring. You would see a wave travel along the spring as it
bunches up in some spots and stretches in others, as shown in
Figure 7.
As a wave passes along the spring, a ribbon tied to one of the
coils of the spring will move back and forth, parallel to the direction that the wave travels. Waves that cause the particles in a
medium to vibrate parallel to
the direction of wave motion
are called longitudinal waves.
Sound waves are an example
Particle motion
of longitudinal waves that we
encounter every day. Sound
waves traveling in air compress
Wave motion
and expand the air in bands. As
sound waves pass by molecules
in the air move backward and
forward parallel to the direction
that the sound travels.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
transverse wave a wave
in which the particles of the
medium move perpendicular
to the direction the wave is
traveling
▲
Longitudinal waves have parallel motion
▲
When a crowd does “the wave” at a sporting event, people in the
crowd stand up and raise their hands into the air as the wave
reaches their part of the stadium. The wave travels around the stadium in a circle, but the people move straight up and down. This
is similar to the wave in the rope. Each particle in the rope moves
straight up and down as the wave passes by from left to right.
In these cases, the motion of the particles in the medium (in
the stadium, the people in the crowd) is perpendicular to the
motion of the wave as a whole. Waves in which the motion of the
particles is perpendicular to the motion of the wave as a whole
are called transverse waves.
Light waves are another example of transverse waves. The
fluctuating electric and magnetic fields that make up a light wave
are perpendicular to one another and are also perpendicular to
the direction the light travels.
ACTIVITY
longitudinal wave a wave
in which the particles of the
medium vibrate parallel to the
direction of wave motion
Figure 7
As a longitudinal wave passes
along this spring, the ribbon tied
to the coils moves back and forth,
parallel to the direction the wave
is traveling.
WAVES
461
In a surface wave, particles move in circles
Waves on the ocean or in a swimming pool are not
simply transverse waves or longitudinal waves.
Water waves are an example of surface waves.
Surface waves occur at the boundary between two
different mediums, such as between water and air.
The particles in a surface wave move both perpendicularly and parallel to the direction that the
wave travels.
Follow the motion of the beach ball in
Figure 8 as a wave passes by traveling from left
to right. At first, the ball is in a trough. As the
crest approaches, the ball moves to the left and
upward. When the ball is very near the crest, it
starts to move to the right. Once the crest has
passed, the ball starts to fall back downward,
then to the left. The up and down motions combine with the side to side motions to produce a
circular motion overall.
The beach ball helps to make the motion of
the wave more visible. Particles near the surface of
the water also move in a similar circular pattern.
Figure 8
Ocean waves are surface waves at the
boundary between air and water.
SECTION 1 REVIEW
SU M MARY
> A wave is a disturbance
that carries energy through
a medium or through space.
> Mechanical waves require
a medium through which
to travel. Light waves, also
called electromagnetic
waves, do not require
a medium.
> Particles in a medium may
vibrate perpendicularly to
or parallel to the direction
a wave is traveling.
462
C H A P T E R
1 4
1. Identify the medium for the following waves:
a. ripples on a pond
b. the sound waves from a stereo speaker
c. seismic waves
2. Name the one kind of wave that does not require a medium.
3. Describe the motion of a mass vibrating on a spring. How
does this relate to wave motion?
4. Explain the difference between transverse waves and longitudinal waves. Give an example of each type.
5. Describe the motion of a water molecule on the surface of
the ocean as a wave passes by.
6. Critical Thinking Describe a situation that demonstrates that
water waves carry energy.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
SECTION
2
Characteristics of Waves
>
>
>
>
▲
OBJECTIVES
KEY TERMS
crest
trough
amplitude
wavelength
period
frequency
Doppler effect
Identify the crest, trough, amplitude, and wavelength
of a wave.
Define the terms frequency and period.
Solve problems involving wave speed, frequency,
and wavelength.
Describe the Doppler effect.
I
f you have spent any time at the beach or on a boat, you have
probably observed many properties of waves. Sometimes the
waves are very large; other times they are smaller. Sometimes they
are close together, and sometimes they are farther apart. How can
these differences be described and measured in more detail?
Wave Properties
The simplest transverse waves have somewhat similar shapes no
matter how big they are or what medium they travel through. An
ideal transverse wave has the shape of a sine curve, such as the
curve on the graph in Figure 9A. A sine curve looks like an S lying
on its side. Sine curves can be used to represent waves and to
describe their properties.
Waves that have the shape of a sine curve, such as those on
the rope in Figure 9B, are called sine waves. Although many
waves, such as water waves, are not ideal sine waves, they can
still be modeled with the graph of a sine curve.
Figure 9
A A sine curve can be used to demonstrate
B This transverse wave on a rope
the characteristics of waves.
is a simple sine wave.
Crest
Displacement
Wavelength
Wavelength
Amplitude
Trough
Copyright © by Holt, Rinehart and Winston. All rights reserved.
WAVES
463
Amplitude measures the amount of particle vibration
Density
The highest points of a transverse wave are called crests. The
lowest parts of a transverse wave are called troughs. The greatDisc Two, Module 12:
est distance that particles are displaced from their normal resting
Frequency and Wavelength
Use the Interactive Tutor to learn more
positions because of a wave is called the amplitude. The ampliabout these topics.
tude is also half the vertical distance between a crest and a trough.
Larger waves have bigger amplitudes and carry more energy.
But what about longitudinal waves? These waves do
Compression
A
not have crests and troughs because they cause particles
Rarefaction
to move back and forth instead of up and down. If you
make a longitudinal wave in a spring, you will see a
moving pattern of areas where the coils are bunched up
alternating with areas where the coils are stretched out.
B
The crowded areas are called compressions. The
stretched-out areas are called rarefactions. Figure 10A
illustrates these properties of a longitudinal wave.
Figure 10B shows a graph of a longitudinal wave.
Density of the medium is plotted on the vertical axis; the
Figure 10
horizontal axis represents the distance along the spring.
A A longitudinal wave has compressions
The result is a sine curve. The amplitude of a longitudiand rarefactions.
nal wave is the maximum deviation from the normal
B The high and low points of this sine
density or pressure of the medium, which is shown by
curve correspond to compressions and
the high and low points on the graph.
rarefactions in the spring.
Wavelength measures the distance between two equivalent
parts of a wave
▲
crest the highest point
of a wave
▲
trough the lowest point
of a wave
▲
amplitude the maximum
distance that the particles
of a wave’s medium vibrate
from their rest position
▲
wavelength the distance
from any point on a wave
to an identical point on the
next wave
464
C H A P T E R
1 4
The crests of ocean waves at a beach may be separated by several
meters, while ripples in a pond may be only a few centimeters
apart. Crests of a light wave may be separated by only billionths
of a meter.
The distance from one crest of a wave to the next crest, or
from one trough to the next trough, is called the wavelength. In
a longitudinal wave, the wavelength is the distance between two
compressions or between two rarefactions. The wavelength is the
distance between any two successive identical parts of a wave.
Not all waves have a single wavelength that is easy to measure.
Most sound waves have a very complicated shape, so the wavelength may be difficult to determine. If the source of a wave
vibrates in an irregular way, the wavelength may change over time.
When used in equations, wavelength is represented by the
Greek letter lambda, l. Because wavelength is a distance measurement, it is expressed in the SI unit meters.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
The period measures how long it takes for waves to pass by
▲
period the time that it takes
a complete cycle or wave
oscillation to occur
▲
If you swim out into the ocean until your feet can no longer touch
the bottom, your body will be free to move up and down as waves
come into shore. As your body rises and falls, you can count off
the number of seconds between two successive wave crests.
The time required for one full wavelength of a wave to pass a
certain point is called the period of the wave. The period is also
the time required for one complete vibration of a particle in a
medium—or of a swimmer in the ocean. In equations, the period
is represented by the symbol T. Because the period is a time
measurement, it is expressed in the SI unit seconds.
frequency the number of
cycles or vibrations per unit
of time
Frequency measures the rate of vibrations
While swimming in the ocean or floating in an
inner tube, as shown in Figure 11, you could
also count the number of crests that pass by in
a certain time, say in 1 minute. The frequency
of a wave is the number of full wavelengths that
pass a point in a given time interval. The frequency of a wave also measures how rapidly
vibrations occur in the medium, at the source
of the wave, or both.
The symbol for frequency is f. The SI unit
for measuring frequency is hertz (Hz), named
after Heinrich Hertz, who in 1888 became the
first person to experimentally demonstrate the
existence of electromagnetic waves. Hertz units
measure the number of vibrations per second.
One vibration per second is 1 Hz, two vibrations per second is 2 Hz, and so on. You can
hear sounds with frequencies as low as 20 Hz and as high as 20
000 Hz. When you hear a sound at 20 000 Hz, there are 20 000
compressions hitting your ear every second.
The frequency and period of a wave are related. If more vibrations are made in a second, each one takes a shorter amount of
time. In other words, the frequency is the inverse of the period.
t0s
t1s
t2s
Figure 11
A person floating in an inner tube
can determine the period and
frequency of the waves by counting off the number of seconds
between wave crests.
Frequency-Period Equation
1
frequency = period
1
f=
T
In the inner tube example, a wave crest passes the inner tube
every 2 s, so the period is 2 s. The frequency can be found by using
the frequency-period equation above. Because 0.5 (1/2) is the
inverse of 2, the frequency is 0.5 Hz, or half a wave per second.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
WAVES
465
Frequency (ⴛ1014 Hz)
4.3
5.0
6.0
Wavelength (nm)
700
600
500
Infrared
Red
Orange
Yellow
Green
7.5
400
Blue
Violet
Ultraviolet
Figure 12
The part of the electromagnetic
spectrum that we can see is called
visible light.
Light comes in a wide range of frequencies and wavelengths
Our eyes can detect light with frequencies ranging from about
4.3 1014 Hz to 7.5 1014 Hz. Light in this range is called visible
light. The differences in frequency in visible light account for the
different colors we see, as shown in Figure 12.
Electromagnetic waves also exist at other frequencies that we
cannot see directly. The full range of light at different frequencies
and wavelengths is called the electromagnetic spectrum. Table 1
lists several different parts of the electromagnetic spectrum,
along with some real-world applications of the different kinds
of waves.
Table 1
The Electromagnetic Spectrum
Type of wave
Range of frequency and wavelength
f < 1 × 109 Hz
λ > 30 cm
Radio wave
1 × 109 Hz < f < 3 × 1011 Hz
30 cm > λ > 1 mm
Microwave
3 × 1011 Hz < f < 4.3 × 1014 Hz
1 mm > λ > 700 nm
Infrared (IR) wave
Applications
AM and FM radio; television
broadcasting; radar; aircraft
navigation
Atomic and molecular research;
microwave ovens
Infrared photography; remotecontrol devices; heat radiation
Visible light
4.3 × 1014 Hz < f < 7.5 × 1014 Hz
700 nm (red) > λ > 400 nm (violet)
Visible-light photography; optical
microscopes; optical telescopes
Ultraviolet (UV) light
7.5 × 1014 Hz < f < 5 × 1015 Hz
400 nm > λ > 60 nm
Sterilizing medical instruments;
identifying fluorescent minerals
X ray
5 × 1015 Hz < f < 3 × 1021 Hz
−
60 nm > λ > 1 × 10 4 nm
Medical examination of bones,
teeth, and organs; cancer
treatments
Gamma ray
3 × 1018 Hz < f < 3 × 1022 Hz
−
0.1 nm > λ > 1 × 10 5 nm
Food irradiation; studies of
structural flaws in thick materials
466
C H A P T E R
1 4
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Wave Speed
Imagine watching as water waves move past a post at a pier such
as the one in Figure 13. If you count the number of crests passing
the post for 10 s, you can determine the frequency of the waves
by dividing the number of crests you count by 10 s. If you measure the distance between crests, you can find the wavelength of
the wave. But how fast are the water waves moving?
Wave speed equals frequency times wavelength
The speed of a moving object is found by dividing the distance
the object travels by the time it takes to travel that distance.
Speed can be calculated using the speed equation:
distance
speed = time
Figure 13
By observing the frequency and
wavelength of waves passing a
pier, you can calculate the speed
of the waves.
d
v=
t
If SI units are used for measuring distance and time, speed is
expressed as meters per second (m/s). The wave speed is simply
how fast a wave moves. Finding the speed of a wave is just like
finding the speed of a moving object: you need to measure how
far the wave travels in a certain amount of time.
For a wave, it is most convenient to use the wavelength as the
distance traveled. The amount of time it takes the wave to travel
a distance of one wavelength is the period. Substituting these
into the speed equation gives an equation that can be used to calculate the speed of a wave.
wavelength
speed = period
l
v= T
Because the period is the inverse of the frequency, dividing by
the period is equivalent to multiplying by the frequency.
Therefore, the speed of a wave can also be calculated by multiplying the wavelength by the frequency.
Wave Speed Equation
wave speed = frequency × wavelength
v=f×l
Suppose that waves passing by a post at a pier have a wavelength of 10 m, and two waves pass by in 5 s. The period is therefore 2.5 s, and the frequency is the inverse of 2.5 s, or 0.4 Hz. The
waves in this case travel with a wave speed of 4 m/s.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
EARTH SCIENCE
Earthquakes create
waves, called seismic
waves, that travel
through Earth. There
are two main types of seismic
waves, P waves (primary
waves) and S waves (secondary waves).
P waves travel faster than
S waves, so the P waves arrive
at a given location first. P waves
are longitudinal waves that tend
to shake the ground from side
to side.
S waves move more slowly
than P waves but also carry
more energy. S waves are
transverse waves that shake
the ground up and down, often
damaging buildings and roads.
WAVES
467
Math Skills
Practice
Wave Speed The string of a piano that produces the note mid-
HINT
dle C vibrates with a frequency of 264 Hz. If the sound waves
produced by this string have a wavelength in air of 1.30 m,
what is the speed of sound in air?
> When a problem requires you
to calculate wave speed, you
can use the wave speed equation on the previous page.
> The wave speed equation can
also be rearranged to isolate
frequency on the left in the
following way:
v=f×l
Divide both sides by l.
v f×l
= l
l
1
List the given and unknown values.
Given: frequency, f = 264 Hz
wavelength, l = 1.30 m
Unknown: wave speed, v = ? m/s
2
Write the equation for wave speed.
v=f×l
3
Insert the known values into the equation, and solve.
v = 264 Hz × 1.30 m = 264 s−1 × 1.30 m
v = 343 m/s
v
l
f= You will need to use this form
of the equation in Practice
Problem 3.
> In Practice Problem 4, you
will need to rearrange the
equation to isolate wavelength on the left.
Practice
Wave Speed
1. The average wavelength in a series of ocean waves is 15.0 m.
A wave crest arrives at the shore on average every 10.0 s, so the
frequency is 0.100 Hz. What is the average speed of the waves?
2. An FM radio station broadcasts electromagnetic waves at a
frequency of 94.5 MHz (9.45 × 107 Hz). These radio waves have
a wavelength of 3.17 m. What is the speed of the waves?
3. Green light has a wavelength of 5.20 × 10−7 m. The speed of
light is 3.00 × 108 m/s. Calculate the frequency of green light
waves with this wavelength.
4. The speed of sound in air is about 340 m/s. What is the
wavelength of a sound wave with a frequency of 220 Hz
(on a piano, the A below middle C)?
The speed of a wave depends on the medium
Sound waves can travel through air. If they couldn’t, you would
not be able to have a conversation with a friend or hear music
from a radio across the room. Because sound travels very fast in
air (about 340 m/s), you don’t notice a time delay in most normal
situations.
If you swim with your head underwater, you may hear certain
sounds very clearly. Sound waves travel better—and three to four
times faster—in water than in air. Dolphins, such as those in
Figure 14, use sound waves to communicate with one another
over long distances underwater. Sound waves travel even faster
in solids than in air or in water. Sound waves have speeds 15 to
20 times faster in rock or metal than in air.
468
C H A P T E R
1 4
Copyright © by Holt, Rinehart and Winston. All rights reserved.
If someone strikes a long steel rail with
a hammer at one end and you listen for the
sound at the other end, you might hear two
bangs. The first sound comes through the
steel rail itself and reaches you shortly
before the second sound, which travels
through the air.
The speed of a wave depends on the
medium. In a given medium, though, the
speed of waves is constant; it does not
depend on the frequency of the wave. No
matter how fast you shake your hand up
and down to create waves on a rope, the
waves will travel the same speed. Shaking
your hand faster just increases the frequency and decreases the wavelength.
Kinetic theory explains differences in wave speed
The arrangement of particles in a medium determines how well
waves travel through it. The different states of matter are due to
different degrees of organization at the particle level.
In gases, the molecules are far apart and move around randomly. A molecule must travel through a lot of empty space
before it bumps into another molecule. Waves don’t travel as fast
in gases.
In liquids, such as water, the molecules are much closer
together. But they are also free to slide past one another. As a
result, vibrations are transferred more quickly from one molecule to the next than they are in a gas. This situation can be compared to vibrating masses on springs that are so close together
that the masses rub against each other.
In a solid, molecules are not only closer together but also
tightly bound to each other. The effect is like having vibrating
masses that are glued together. When one mass starts to vibrate,
all the others start to vibrate almost immediately. As a result,
waves travel very quickly through most solids.
Figure 14
Dolphins use sound waves to
communicate with one another.
Sound travels three to four times
faster in water than in air.
Quick
Quick
Wave Speed
1. Place a rectangular pan
2.
on a level surface, and
fill the pan with water to
a depth of about 2 cm.
Cut a wooden dowel (3
cm in diameter or
thicker) to a length
slightly less than the
width of the pan, and
place the dowel in one
end of the pan.
Move or roll the dowel
slowly back and forth,
and observe the length
of the wave generated.
Now move the dowel
back and forth faster
(increased frequency).
How does that affect the
wavelength?
Do the waves always
travel the same speed in
the pan?
Quick
3.
Light has a finite speed
4.
When you flip a light switch, light seems to fill the room instantly.
However, light does take time to travel from place to place. All
electromagnetic waves in empty space travel at the same speed,
the speed of light, which is 3.00 108 m/s (186 000 mi/s). The
speed of light in empty space is a constant that is often represented
by the symbol c. Light travels slower when it has to pass through
a medium such as air or water.
5.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
ACTIVITY
WAVES
469
The Doppler Effect
Imagine that you are standing on a corner as an ambulance
rushes by. As the ambulance passes, the sound of the siren
changes from a high pitch to a lower pitch. Why? Do the sound
waves produced by the siren change as the ambulance goes by?
How does the motion of the ambulance affect the sound?
Pitch is determined by the frequency of sound waves
The pitch of a sound, how high or low it is, is determined by the
frequency at which sound waves strike the eardrum in your ear.
A higher-pitched sound is caused by sound waves of higher frequency. As you know from the wave speed equation, frequency
and wavelength are also related to the speed of a wave.
Suppose you could see the sound waves from the ambulance
siren when the ambulance is at rest. You would see the sound
waves traveling out from the siren in circular wave fronts, as
shown in Figure 15A. The distance between two successive wave
fronts shows the wavelength of the sound waves. When the sound
waves reach your ears, they have a frequency equal to the number of wave fronts that strike your eardrum each second. That
frequency determines the pitch of the sound that you hear.
Figure 15
Observer
A
A When an ambulance is not moving, the sound
waves produced by the siren spread out in circles.
The frequency of the waves is the same at any
location.
470
C H A P T E R
1 4
Observer
B
B When an ambulance is moving, the sound waves
produced by the siren are closer together in front
and farther apart behind. Observer A hears a
higher-pitched sound than Observer B hears.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Frequency changes when the source of waves is moving
www.scilinks.org
Topic: Doppler Effect
SciLinks code: HK4032
▲
If the ambulance is moving toward you, the sound waves from
the siren are compressed in the direction of motion, as shown in
Figure 15B. Between the time that one sound wave and the next
sound wave are emitted by the siren, the ambulance moves a
short distance. This shortens the distance between wave fronts,
while the wave speed remains the same. As a result, the sound
waves reach your ear at a higher frequency.
Because the waves now have a higher frequency, you hear a
higher-pitched sound than you would if the ambulance were at
rest. Similarly, if the ambulance were moving away from you, the
frequency at which the waves reached your ear would be less
than if the ambulance were at rest, and you would hear the sound
of the siren at a lower pitch. This change in the observed frequency of a wave resulting from the motion of the source or
observer is called the Doppler effect. The Doppler effect occurs
for light and other types of waves as well.
Doppler effect an observed
change in the frequency of a
wave when the source or
observer is moving
SECTION 2 REVIEW
SU M MARY
> The highest points of a
transverse wave are called
crests; the lowest parts are
called troughs.
> The amplitude of a transverse wave is half the vertical distance between a
crest and a trough.
> The wavelength is the distance between two identical parts of a wave.
> The period of a wave is the
time it takes a wavelength
to pass a certain point.
1. Draw a sine curve, and label a crest, a trough, and the
amplitude.
2. State the SI units used for wavelength, period, frequency,
and wave speed.
3. Describe how the frequency and period of a wave are related.
4. Explain why sound waves travel faster in liquids or solids
than in air.
5. Critical Thinking What happens to the wavelength of a wave
when the frequency of the wave is doubled but the wave
speed stays the same?
6. Critical Thinking Imagine you are waiting for a train to pass at
a railroad crossing. Will the train whistle have a higher pitch
as the train approaches you or after it has passed you by?
Practice
> The frequency of a wave is
the number of vibrations
that occur in a given
amount of time. (1 Hz 1 vibration/s)
> The speed of a wave
equals the frequency times
the wavelength. (v f l)
7. A wave along a guitar string has a frequency of 440 Hz and
a wavelength of 1.5 m. What is the speed of the wave?
8. The speed of sound in air is about 340 m/s. What is the
wavelength of sound waves produced by a guitar string
vibrating at 440 Hz?
9. The speed of light is 3 108 m/s. What is the frequency of
microwaves with a wavelength of 1 cm?
Copyright © by Holt, Rinehart and Winston. All rights reserved.
WAVES
471
SECTION
3
Wave Interactions
▲
OBJECTIVES
KEY TERMS
reflection
diffraction
refraction
interference
constructive interference
destructive interference
standing wave
>
>
>
>
Describe how waves behave when they meet an obstacle
or pass into another medium.
Explain what happens when two waves interfere.
Distinguish between constructive interference and
destructive interference.
Explain how standing waves are formed.
W
hen waves are simply moving through a medium or
through space, they may move in straight lines like waves
on the ocean, spread out in circles like ripples on a pond, or
spread out in spheres like sound waves in air. But what happens
when a wave meets an object or another wave in the medium?
And what happens when a wave passes into another medium?
Disc Two, Module 13: Reflection
Use the Interactive Tutor to learn more
about this topic.
Reflection, Diffraction, and Refraction
▲
You probably already know what happens when light waves
strike a shiny surface: they reflect off the surface. Other waves
reflect, too. Figure 16 shows two ways that a wave on a rope may
be reflected. Reflection is simply the bouncing back of a wave
when it meets a surface or boundary.
reflection the bouncing
back of a ray of light, sound,
or heat when the ray hits a
surface that it does not go
through
A
B Original wave
Original wave
Figure 16
A If the end of a rope is
free to slide up and down
a post, a wave on the
rope will reflect from the
end.
B If the end of the rope
is fixed, the reflected
wave is turned upside
down.
Reflected
wave
Reflected
wave
472
C H A P T E R
1 4
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Waves reflect at a free boundary
Figure 16A shows the reflection of a single wave traveling on a
rope. The end of the rope is free to move up and down on a post.
When the wave reaches the post, the loop on the end moves up
and then back down. This is just what would happen if someone
were shaking that end of the rope to create a new wave. The
reflected wave in this case is exactly like the original wave except
that the reflected wave is traveling in the opposite direction to
the direction of the original wave.
www.scilinks.org
Topic: Reflection, Refraction, Diffraction
SciLinks code: HK4119
At a fixed boundary, waves reflect and turn upside down
Figure 16B shows a slightly different situation. In this case, the
▲
end of the rope is not free to move because it is attached to a wall.
When the wave reaches the wall, the rope exerts an upward force
on the wall. The wall is too heavy to move, but it exerts an equal
and opposite downward force on the rope, following Newton’s
third law. The force exerted by the wall causes another wave to
start traveling down the rope. This reflected wave travels in the
opposite direction and is turned upside down.
diffraction a change in the
direction of a wave when the
wave finds an obstacle or an
edge, such as an opening
Diffraction is the bending of waves around an edge
If you stand outside the doorway of a classroom, you
may be able to hear the sound of voices inside the room.
But if the sound waves cannot travel in a straight line to
your ear, how are you able to hear the voices?
When waves pass the edge of an object or pass
through an opening, such as an open window or a door,
they spread out as if a new wave were created there. In
effect, the waves seem to bend around an object or
opening. This bending of waves as they pass an edge is
called diffraction.
Figure 17A shows waves passing around a block in a
tank of water. Before they reach the block, the waves
travel in a straight line. After they pass the block, the
waves near the edge bend and spread out into the space
behind the block. Diffraction is the reason that shadows
never have perfectly sharp edges.
The tank in Figure 17B contains two blocks placed
end to end with a small gap in between. In this case,
waves bend around two edges and spread out as they
pass through the opening. Sound waves passing
through a door behave the same way. Because sound
waves spread out into the space beyond the door, a person near the door on the outside can hear sounds from
inside the room.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
A
B
Figure 17
A Waves bend when they pass the edge of
an obstacle.
B When they pass through an opening,
waves bend around both edges.
WAVES
473
Waves can also bend by refraction
Figure 18 shows a spoon in a glass of water. Why does the spoon
Figure 18
Because light waves bend when
they pass from one medium to
another, this spoon looks like it
is in two pieces.
look like it is broken into two pieces? This strange sight results
from light waves bending, but not because of diffraction. This
time, the waves are bending because of refraction. Refraction is
the bending of waves when they pass from one medium into
another. All waves are refracted when they pass from one
medium to another at an angle.
Light waves from the top of the spoon handle pass straight
through the air and the glass from the spoon to your eyes. But the
light waves from the rest of the spoon start out in the water, then
pass into the glass, then into the air. Each time the waves enter a
new medium, they bend slightly because of a change in speed. By
the time those waves reach your eyes, they are coming from a different angle than the waves from the top of the spoon handle. But
your eyes just see that one set of light waves are coming from one
direction, and another set of waves are coming from a different
direction. As a result, the spoon appears to be broken.
▲
refraction the bending of
a wavefront as the wavefront
passes between two substances in which the speed
of the wave differs
▲
interference the combination of two or more waves of
the same frequency that results
in a single wave
Interference
What would happen if you and another person tried to walk
through the exact same place at the same time? You would run
into each other. Material objects, such as a human body, cannot
share space with other material objects. More than one wave,
however, can exist in the same place at the same time.
Figure 19
Water waves passing through each other produce
interference patterns.
474
C H A P T E R
1 4
Waves in the same place combine to produce
a single wave
When several waves are in the same location,
the waves combine to produce a single, new
wave that is different from the original waves.
This is called interference. Figure 19 shows
interference occurring as water waves pass
through each other. Once the waves have
passed through each other and moved on, they
return to their original shape.
You can show the interference of two waves
by drawing one wave on top of another on a
graph, as in Figure 20. The resulting wave can
be found by adding the height of the waves at
each point. Crests are considered positive, and
troughs are considered negative. This method
of adding waves is sometimes known as the
principle of superposition.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
A
First wave
Figure 20
Second wave
Constructive and Destructive
Interference
Resulting wave
A When two waves line up so
their crests overlap, they add
together to make a larger wave.
First wave
Resulting wave
B
Second wave
B When the crest of a large
wave overlaps with the trough
of a smaller wave, subtraction
occurs.
C Two waves of the same size
First wave
may completely cancel each other
out.
Resulting wave
C
Second wave
Constructive interference increases amplitude
Disc Two, Module 14: Refraction
Use the Interactive Tutor to learn more
about this topic.
▲
When the crest of one wave overlaps the crest of another wave,
the waves reinforce each other, as shown in Figure 20A. Think
about what happens at the particle level. Suppose the crest of one
wave would move a particle up 4 cm from its original position,
and another wave crest would move the particle up 3 cm.
When both waves hit at the same time, the particle moves
up 4 cm due to one wave and 3 cm due to the other for a total
of 7 cm. The result is a wave whose amplitude is the sum of
the amplitudes of the two individual waves. This is called
constructive interference.
any interference in which
waves combine so that the
resulting wave is bigger than
the original waves
Destructive interference decreases amplitude
Copyright © by Holt, Rinehart and Winston. All rights reserved.
▲
When the crest of one wave meets the trough of another wave,
the resulting wave has a smaller amplitude than the larger
of the two waves, as shown in Figure 20B. This is called
destructive interference.
To understand how this works, imagine again a single particle. Suppose the crest of one wave would move the particle up 4
cm, and the trough of another wave would move it down 3 cm. If
the waves hit the particle at the same time, the particle would
move in response to both waves, and the new wave would have
an amplitude of just 1 cm. When destructive interference occurs
between two waves that have the same amplitude, the waves may
completely cancel each other out, as shown in Figure 20C.
constructive interference
destructive interference
any interference in which
waves combine so that the
resulting wave is smaller than
the largest of the original waves
WAVES
475
Interference of light waves creates colorful displays
The interference of light waves often produces colorful displays.
You can see a rainbow of colors when oil is spilled onto a watery
surface. Soap bubbles, like the ones shown in Figure 21, have
reds, blues, and yellows on their surfaces. The colors in these
examples are not due to pigments or dyes. Instead, they are due
to the interference of light.
When you look at a soap bubble, some light waves bounce off
the outside of the bubble and travel directly to your eye. Other
light waves travel into the thin shell of the bubble, bounce off the
inner side of the bubble’s shell, then travel back through the shell,
into the air and to your eye. Those waves travel farther than the
waves reflected directly off the outside of the bubble. At times the
two sets of waves are out of step with each other. The two sets of
waves interfere contructively at some frequencies (colors) and
destructively at other frequencies (colors). The result is a swirling
rainbow effect.
Figure 21
The colorful swirls on a bubble
result from the constructive
interference of some colors and
the destructive interference of
other colors.
Interference of sound waves produces beats
The sound waves from two tuning forks of slightly different
frequencies will interfere with each other as shown in Figure 22A.
Because the frequencies of the tuning forks are different, the
compressions arrive at your ear at different rates.
When the compressions from the two tuning forks arrive at
your ear at the same time, constructive interference occurs, and
the sound is louder. A short time later, the compression from one
and the rarefaction from the other arrive together. When this
happens, destructive interference occurs, and a softer sound is
heard. After a short time, the compressions again arrive at the
same time, and again a loud sound is heard. Overall, you hear a
series of loud and soft sounds called beats.
Figure 22
A When two waves of slightly
different frequencies interfere with
each other, they produce beats.
B A piano tuner can listen for
beats to tell if a string is out
of tune.
t1
t2
t3
Destructive
interference
Constructive
interference
Destructive
interference
B
A
476
C H A P T E R
1 4
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Figure 22B shows a piano tuner tuning a
string. Piano tuners listen for beats between a
tuning fork of known frequency and a string on
a piano. By adjusting the tension in the string,
the tuner can change the pitch (frequency) of
the string’s vibration. When no beats are heard,
the string is vibrating with the same frequency
as the tuning fork. In that case, the string is said
to be in tune.
Standing Waves
Waves can also interfere in another way.
Suppose you send a wave through a rope tied to
a wall at the other end. The wave is reflected
from the wall and travels back along the rope.
If you continue to send waves down the rope,
the waves that you make will interfere with
those waves that reflect off the wall and travel
back toward you.
Interference can cause standing waves
Standing waves can form when a wave is
reflected at the boundary of a medium. In a
standing wave, interference of the original
wave with the reflected wave causes the
medium to vibrate in a stationary pattern that
resembles a loop or a series of loops. Although
it appears as if the wave is standing still, in reality waves are traveling in both directions.
Connection to
ARCHITECTURE
ARCHITECTURE
Y
ou might have experienced destructive interference in an auditorium or a concert hall.
As sound waves reflect from the walls, there are
places, known as dead spots, where the waves
interfere destructively and cancel out.
Dead spots are produced by the interference
of sound waves coming directly from the stage
and waves reflected off the walls. For this reason,
architects design concert halls so that the dimensions are not simple multiples of each other.
They also try to avoid smooth, parallel walls in
the design. Irregularities in the wall and ceiling
contribute to reducing the direct reflections of
waves and the possible resulting interference.
Making the Connection
1. With a friend, go to a square or rectangular
room with walls made of brick, cinder block,
or concrete. Have one person talk or sing
loudly while the other person moves around
the room to locate dead spots.
2. Draw an overhead view of the room, and
mark the locations of the dead spots. Why do
you think the dead spots are in those places?
3. Write a short paragraph explaining
how the room could be changed
to reduce or eliminate the dead
spots.
WRIT
ING
SKIL
L
Standing waves have nodes and antinodes
Copyright © by Holt, Rinehart and Winston. All rights reserved.
▲
Each loop of a standing wave is separated from the next loop by
points that have no vibration, called nodes. Nodes lie at the
points where the crests of the original waves meet the troughs of
the reflected waves, causing complete destructive interference.
One of the nodes on a fixed rope lies at the point of reflection,
where the rope cannot vibrate. Another node is near your hand.
If you shake the rope up and down at the right frequency, you can
create standing waves with several nodes along the length of the
string.
Midway between the nodes lie points of maximum vibration,
called antinodes. Antinodes form where the crests of the original
waves line up with the crests of the reflected waves so that complete constructive interference occurs.
standing wave a pattern of
vibration that simulates a wave
that is standing still
WAVES
477
Standing waves can have only certain
wavelengths
Figure 23 shows several different possible stand-
Figure 23
These photos of standing waves were captured
using a strobe light that flashes different colors
at different times.
ing waves on a string fixed at both ends. Only a
few waves with specific wavelengths can form
standing waves in any given string.
The simplest standing waves occur when the
wavelength of the waves is twice the length of the
string. In that case, it just looks like the entire
string is shaking up and down. The only nodes
are on the two ends of the string.
If the string vibrates with a higher frequency,
the wavelength becomes shorter. At a certain frequency, the wavelength is exactly equal to the
length of the string. In the middle of the string,
complete destructive interference occurs, producing a node.
In general, standing waves can exist whenever
a multiple of half-wavelengths will fit exactly in
the length of the string. It is even possible for
standing waves of more than one wavelength to
exist on a string at the same time.
SECTION 3 REVIEW
SU M MARY
> Waves bouncing off a surface is called reflection.
> Diffraction is the bending
of waves as they pass an
edge or corner.
1. Describe what may happen when ripples on a pond
encounter a large rock in the water.
2. Explain why you can hear two people talking even after they
walk around a corner.
3. Name the conditions required for two waves to interfere
constructively.
> Refraction is the bending of
4. Explain why colors appear on the surface of a soap bubble.
waves as they pass from
one medium to another.
5. Draw a standing wave, and label the nodes and antinodes.
> Interference results when
two waves exist in the
same place and combine
to make a single wave.
> Interference may cause
standing waves.
6. Critical Thinking What conditions are required for two
waves on a rope to interfere completely destructively?
7. Critical Thinking Imagine that you and a friend are trying to
tune the lowest strings on two different guitars to the same
pitch. Explain how you could use beats to determine if the
strings are tuned to the same frequency.
8. Critical Thinking Determine the longest possible wavelength
of a standing wave on a string that is 2 m long.
478
C H A P T E R
1 4
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Graphing Skills
Displacement (cm)
Displacement (cm)
Interpreting Graphs
5
0.005
0.01
-5
0.015
0.02
0.025
0.03
40
50
60
Time (s)
5
10
20
30
-5
Distance (cm)
The graphs above show the behavior of a single transverse wave. Study the graphs, and
answer the following questions.
1
What types of graphs are these?
2
What variable is described in the x-axis of the first
graph? What variable is described in the
x-axis of the second graph?
3
0
0.93
0.25
2.43
0.50
3.00
0.75
2.43
1.00
0.93
1.25
–0.93
1.50
–2.43
1.75
–3.00
2.00
–2.43
2.25
–0.93
Why are both graphs needed to provide complete
information about the wave?
2.50
0.93
2.75
2.43
Plot the data given in the table to the right. From the
graph, calculate the wavelength and amplitude of the
wave.
3.00
3.00
What information about the wave is indicated by the
first graph? What information is indicated by the second graph?
4
Determine from the graphs the period, amplitude,
and wavelength of the wave.
5
Using the frequency-period equation, calculate the
frequency of the wave. Use the wave speed equation
to calculate the speed of the wave.
6
7
x-axis (cm) y-axis (cm)
Copyright © by Holt, Rinehart and Winston. All rights reserved.
GR AP H I NG
SKI LLS
479
C H A P T E R 14
Chapter Highlights
Before you begin, review the summaries of the
key ideas of each section, found at the end of
each section. The key vocabulary terms are
listed on the first page of each section.
U N DE RSTAN DI NG CONC E PTS
1. A wave is a disturbance that transmits
a. matter.
c. energy.
b. particles.
d. a medium.
2. Electromagnetic waves
a. are transverse waves.
b. require a medium.
c. are mechanical waves.
d. are longitudinal waves.
3. The speed of a wave depends on the
a. medium.
c. amplitude.
b. frequency.
d. wavelength.
4. Waves that need a medium in which to
travel are called
a. longitudinal waves.
b. transverse waves.
c. mechanical waves.
d. All of the above.
5. Most waves are caused by
a. velocity.
c. a vibration.
b. amplitude.
d. earthquakes.
6. For which type of waves do particles in the
medium vibrate perpendicular to the direction in which the waves are traveling?
a. transverse waves
b. longitudinal waves
c. P waves
d. none of the above
7. A sound wave is an example of
a. an electromagnetic wave.
b. a transverse wave.
c. a longitudinal wave.
d. a surface wave.
480
C H A P T E R
1 4
REVIEW
8. In an ocean wave, the molecules of water
a. move perpendicular to the direction of
wave travel.
b. move parallel to the direction of wave
travel.
c. move in circles.
d. don’t move at all.
9. Half the vertical distance between the crest
and trough of a wave is called the
a. frequency.
c. wavelength.
b. crest.
d. amplitude.
10. The number of waves passing a given point
per unit of time is called the
a. frequency.
c. wavelength.
b. wave speed.
d. amplitude.
11. The Doppler effect of a passing siren results
from an apparent change in
a. loudness.
c. frequency.
b. wave speed.
d. interference.
12. The combining of waves as they meet is
known as
a. a crest.
c. interference.
b. noise.
d. the Doppler effect.
13. Waves bend when they pass through an
opening. This is called
a. interference.
c. refraction.
b. diffraction.
d. the Doppler effect.
14. Refraction occurs whenever
a. a wave passes from one medium to
another at an angle.
b. two waves interfere with one another.
c. a wave is reflected at a free boundary.
d. standing waves occur.
15. The Greek letter l is often used to represent
a wave’s
a. period.
c. frequency.
b. wavelength.
d. amplitude.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
US I NG VOC AB U L ARY
16. How would you describe the amplitude of
a wave using the words crest and trough?
17. Explain the difference between waves bending due to refraction and diffraction.
18. Imagine you are shaking the end of a rope
to create a series of waves. What will you
observe if you begin shaking the rope more
quickly? Use the terms wave speed, frequency,
and wavelength in your answer.
19. Describe the changes in elastic potential
energy and kinetic energy that occur when
a mass vibrates on a spring.
20. Use the kinetic theory to explain the difference in wave speed in solids, liquids, and
gases.
21. Why is the reflection of a wave at a free
boundary different from reflection at a
fixed boundary?
27. Imagine a train approaching a crossing where
you are standing safely behind the gate. Explain the changes in sound of the horn that
you may hear as the train passes. Use the
following terms in your answer: frequency,
wavelength, wave speed, and Doppler effect.
28. Draw a picture of a standing wave, and label
a node and an antinode.
B U I LDI NG M ATH S KI LLS
29. Wave Speed Suppose you tie one end of
a rope to a doorknob and shake the other
end with a frequency of 2 Hz. The waves
you create have a wavelength of 3 m. What
is the speed of the waves along the rope?
30. Wave Speed Ocean waves are hitting a
beach at a rate of 2.0 Hz. The distance
between wave crests is 1.5 m. Calculate
the speed of the waves.
23. How is an electromagnetic wave different
from a mechanical wave?
31. Wavelength All electromagnetic waves
have the same speed in empty space,
3.00 108 m/s. Using that speed, find the
wavelengths of the electromagnetic waves
at the following frequencies:
a. radio waves at 530 kHz
b. visible light at 6.0 1014 Hz
c. X rays at 3.0 1018 Hz
24. You have a long metal rod and a hammer.
How would you hit the metal rod to create
a longitudinal wave? How would you hit it
to create a transverse wave?
32. Frequency Microwaves range in wavelength
from 1 mm to 30 cm. Calculate their range
in frequency. Use 3.00 108 m/s as the
speed of electromagnetic waves.
25. Identify each of the following as a distance
measurement, a time measurement, or
neither.
a. amplitude
d. frequency
b. wavelength
e. wave speed
c. period
33. Wavelength The frequency of radio waves
range from about 3.00 105 Hz to 3.00 107 Hz. What is the range of frequencies
of these waves? Use 3.00 108 m/s as the
speed of electromagnetic waves.
22. How do beats help determine whether
two sound waves are of the same frequency?
Use the terms constructive interference and
destructive interference in your answer.
26. Explain the difference between constructive
interference and destructive interference.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
34. Frequency The note A above middle C on a
piano emits a sound wave with wavelength
0.77 m. What is the frequency of the wave?
Use 340 m/s as the speed of sound in air.
WAVES
481
C H A P T E R 14
B U I LDI NG G R AP H I NG S KI LLS
35. Graphing Draw a sine curve, and label
a crest, a trough, and the amplitude.
36. Interpreting Graphics The wave shown in
the figure below has a frequency of 25.0 Hz.
Find the following values for this wave:
a. amplitude
c. speed
b. wavelength
d. period
18 cm
10.0 cm
TH I N KKII NG C R ITIC ALLY
37. Understanding Systems A friend standing
2 m away strikes two tuning forks at the
same time, one at a frequency of 256 Hz
and the other at 240 Hz. Which sound will
reach your ear first? Explain.
38. Applying Knowledge When you are watching a baseball game, you may hear the crack
of the bat a short time after you see the batter hit the ball. Why does this happen?
(Hint: Consider the relationship between
the speed of sound and the speed of light.)
39. Understanding Systems You are standing
on a street corner, and you hear a fire truck
approaching. Does the pitch of the siren
stay constant, increase, or decrease as it
approaches you? Explain.
40. Applying Knowledge If you yell or clap your
hands while standing at the edge of a large
rock canyon, you may hear an echo a few
seconds later. Explain why this happens.
482
C H A P T E R
1 4
REVIEW
41. Interpreting Graphics Draw the wave that
results from interference between the two
waves shown below.
a.
b.
42. Understanding Systems An orchestra is
playing in a huge outdoor amphitheater, and
thousands of listeners are sitting on a hillside far from the stage. To help those listeners hear the concert, the amphitheater has
speakers halfway up the hill. How could you
improve this system? A computer delays the
signal to the speakers by a fraction of a second. Why is this computer used? Explain
what might happen if the signal were not
delayed at all.
43. Applying Knowledge Dolphins use sound
waves to detect other organisms close by.
How can a dolphin use the Doppler effect to
determine whether an organism is moving
towards it? (Hint: the sound waves dolphins
use can reflect off objects in the water and
create an echo.)
DEV E LOP I NG LI F E/W OR K S KI LLS
44. Applying Knowledge Describe how you
interact with waves during a typical school
day. Document the types of waves you
encounter. Document also how often you
interact with each type of wave. Decide
whether one type of wave is more important
in your life than the other types of waves.
45. Applying Technology With your
COMPU
T
teacher’s help, use a microphone
S K I L ER
L
and an oscilloscope or a CBL
interface to obtain an image of a sound.
Determine the frequency and wavelength of
the sound.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
46. Making Decisions A new car is advertised as
having antinoise technology. The manufacturer claims that inside the car any sounds
are negated. Evaluate the possibility of such
a claim. What would have to be created to
cause destructive interference with any
sound in the car? Do you believe that the
manufacturer is correct in its statement?
47. Working Cooperatively Work with other
classmates to research architectural
acoustics that would affect a restaurant.
Investigate acoustics problems in places
where many people gather. How do oddshaped ceilings, decorative panels, and glass
windows affect echoes? Prepare a model of
your school cafeteria showing what changes
you would make to reduce the level of noise.
48. Applying Knowledge A piano tuner listens
to a tuning fork vibrating at 440 Hz to tune
the string of a piano. He hears beats between
the tuning fork and the piano string. Is the
string in tune? Explain your answer.
I NTEG R ATI NG CONC E PTS
49. Connection to Space Science The Doppler
effect occurs for light waves as well as for
sound waves. Research some of the ways
in which the Doppler effect has helped
astronomers understand the motion of distant galaxies and other objects in deep space.
52. Concept Mapping Copy the unfinished
concept map below onto a sheet of paper.
Complete the map by writing the correct
word or phrase in the lettered boxes.
Waves
are either
or electromagnetic
waves
a.
which
which
require a medium
in which to travel
b.
and can
either be
d.
f.
through
transverse or c.
waves
in which
particles
vibrate
carry
matter
or g.
in which
particles
vibrate
e.
www.scilinks.org
Topic: Seismic Waves SciLinks code: HK4126
50. Connection to Earth Science What is the
medium for seismic waves?
51. Connection to Architecture Explore and
describe research on earthquake-proof
buildings and materials. Evaluate the
impact of this research on society in terms
of building codes and architectural styles in
earthquake-prone areas such as Los Angeles,
San Francisco, and Tokyo.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Art Credits: Fig. 4-5, Uhl Studios, Inc.; Fig. 8, Uhl Studios, Inc.; Fig. 9, Mark Schroeder; Fig. 11,
Uhl Studios, Inc.; Fig. 16, Mark Schroeder; Fig. 20, Uhl Studios, Inc.
Photo Credits: Chapter Opener image of surfer, International Stock Photography; sunset over
beach, Bill Brooks/Masterfile; Fig. 1, SuperStock; Fig. 2, Art Resource, NY; Fig. 3, “Quick Lab,”
Fig. 6-7, Peter Van Steen/HRW; Fig. 13, Joe Devenney/Getty Images/The Image Bank; Fig. 14,
Jeff Hunter/Getty Images/The Image Bank; Fig. 15, Peter Van Steen/HRW; Fig. 17, E. R.
Degginger/Color-Pic, Inc.; Fig. 18, Peter Van Steen/HRW; Fig. 19, E. R. Degginger/Color-Pic, Inc.;
Fig. 21, Michael Freeman/Bruce Coleman, Inc.; Fig. 22, Neil Nissing/Getty Images/FPG International;
Fig. 23, Richard Megna/Fundamental Photographs; “Skills Practice Lab,” Sam Dudgeon/HRW;
“Career Link,” Peter Van Steen/HRW.
WAVES
483
Modeling Transverse
Waves
Procedure
Making Sine Curves with a Sand Pendulum
1. Review the discussion in Section 2 on the use of sine
curves to represent transverse waves.
2. On a blank sheet of paper, prepare a table like the
one shown at right.
Introduction
When a transverse wave model is created with a sand pendulum, what wave
characteristics can you measure?
Objectives
> Create sine curves by pulling paper
under a sand pendulum.
> Measure the amplitude, wavelength,
and period of transverse waves using
sine curves as models.
>
USING SCIENTIFIC METHODS
Form a
hypothesis about how changes to
the experiment may change the
amplitude and wavelength.
> Calculate frequency and wave speed
using your measurements.
Materials
colored sand
masking tape
meterstick
nail
paper or plastic-foam cup
ring stand or other support
rolls of white paper, about 30 cm wide
stopwatch
string and scissors
484
C H A P T E R
1 4
3. Use a nail to puncture a small hole in the bottom of
a paper cup. Also punch two holes on opposite sides
of the cup near the rim. Tie strings of equal length
through the upper holes. Make a pendulum by tying
the strings from the cup to a ring stand or other support. Clamp the stand down at the end of a table, as
shown in the photograph at right. Cover the bottom
hole with a piece of tape, then fill the cup with sand.
SAFETY CAUTION Wear gloves while
handling the nails and punching holes.
4. Unroll some of the paper, and mark off
a length of 1 m using two dotted lines.
Then roll the paper back up, and position the paper
under the pendulum, as shown in the photograph at
right.
5. Remove the tape over the hole. Start the pendulum
swinging as your lab partner pulls the paper perpendicular to the cup’s swing. Another lab partner should
loosely hold the paper roll. Try to pull the paper in a
straight line with a constant speed. The sand should
trace a sine curve on the paper, as in the photograph
at right.
6. As your partner pulls the paper under the pendulum,
start the stopwatch when the sand trace reaches the
first dotted line marking the length of 1 m. When the
sand trace reaches the second dotted line, stop the
watch. Record the time in your table.
7. When you are finished making a curve, stop the pendulum and cover the hole in the bottom of the cup.
Be careful not to jostle the paper; if you do, your trace
may be erased. You may want to tape the paper down.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Length along
paper = 1 m
Time (s)
Average
wavelength (m)
Average
amplitude (m)
Curve 1
Curve 2
Curve 3
8. For the part of the curve between the dotted lines, measure the distance from the first crest to the last crest, then
divide that distance by the total number of crests. Record
your answer in the table under “Average wavelength.”
9. For the same part of the curve, measure the vertical
distance between the first crest and the first trough,
between the second crest and the second trough, and
so on. Add the distances together, then divide by the
number of distances you measured. Record your answer
in the table under “Average amplitude.”
Designing Your Experiment
10. With your lab partners, form a hypothesis about how to make two additional sine
curve traces, one with a different average wavelength than the first trace and one
with a different average amplitude.
11. In your lab report, write down your plan for changing these two factors. Before you
carry out your experiment, your teacher must approve your plan.
Performing Your Experiment
12. After your teacher approves your plan, carry out your experiment. For each curve,
measure and record the time, the average wavelength, and the average amplitude.
13. After each trace, return the sand to the cup and roll the paper back up.
Analysis
1. For each of your three curves, calculate the average speed at which the paper was
pulled by dividing the length of 1 m by the time measurement. This is equivalent
to the speed of the wave that the curve models or represents.
2. For each curve, use the wave speed equation to calculate average frequency.
v
average wave speed
average frequency = f=
average wavelength
l
Conclusions
3. What factor did you change to alter the average wavelength of the curve? Did your
plan work? If so, did the wavelength increase or decrease?
4. What factor did you change to alter the average amplitude? Did your plan work?
Copyright © by Holt, Rinehart and Winston. All rights reserved.
WAVE S
485
CareerLink
CareerLink
CareerLink
Ultrasonographer
“Ultrasound is a
Most people have seen a sonogram showing an
helpful diagnostic
unborn baby inside its mother’s womb. Ultrasound
tool that allows
technologists make these images with an
you to see inside
ultrasound machine, which sends harmless, highthe body without
frequency sound waves into the body. Ultrathe use of X rays.”
sonographers work in hospitals, clinics, and
doctors’ offices. Besides checking on the health
of unborn babies, ultrasonographers
use their tools to help diagnose
cancer, heart disease, and other
health problems. To find out more
Estela Zavala uses an
about this career, read this interultrasound machine
view with Estela Zavala, a registered
to check this man’s
kidneys.
diagnostic medical sonographer
who works at Austin Radiological
Association in Austin, Texas.
What part of your job do
you find most satisfying?
What does an
I like helping people find out what is wrong
ultrasonographer do?
?
?
We scan various organs of the body with an
ultrasound machine to see if there are any
abnormalities. For example, we can check
a gallbladder to see if there are any stones
in it. We already know what healthy organs
look like, so anything unusual shows up in
these pictures. This can help a doctor make
a diagnosis.
?
How does the ultrasound
machine make pictures?
The machine creates high-frequency sound
waves. When the sound waves reflect off
of the organs in the body, the waves strike
a piezoelectric crystal in the detector.
Piezoelectric crystals can convert the pressure energy from the ultrasound wave into
an electrical signal. The ultrasound system
processes the signal to create an image.
486
C A R E E R
L I N K
with them in a noninvasive way. Before
ultrasound, invasive surgery was often the
only option.
?
What is challenging about
your job?
The technology is constantly changing. We
are using ultrasound in more ways than
ever before. For example, we can now create images of veins and arteries.
?
What skills does an
ultrasonographer need?
First you need excellent hand-eye coordination, so you can move the equipment over
the parts of the body you need to image.
You also have to know a lot about all of the
organs in the body. It is very important to
be able to work quickly, because sometimes patients are uncomfortable.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
?
How much training and
education did you receive
before becoming an
ultrasonographer?
After graduating from high school, I went to an
X-ray school to be licensed as an X-ray technologist. A medical background like this is necessary
for entering ultrasound training. First I went to
an intensive 1-month training program, which
involved 2 weeks of hands-on work and
2 weeks of classwork. After that, I worked for a
licensed radiologist for about a year. Finally, I
attended an accredited year-long ultrasound
program at a local community college before
becoming fully licensed.
?
?
Would you recommend ultrasound technology as a career
to students?
Yes, I would recommend it. Just remember that
you must have some medical experience first,
such as being a nurse or an X-ray technician, if
you want to continue into other areas of radiology, like ultrasound.
www.scilinks.org
Topic: Ultrasound
SciLinks code: HK4143
What part of your education
do you think was the most
valuable?
The best part was the on-the-job training that
was involved. You need to do a lot of ultrasounds before you can become proficient.
“I’ve seen many changes and
innovations in ultrasound since
I began. Because of this, the
job always seems new.”
—Estela Zavala
Copyright © by Holt, Rinehart and Winston. All rights reserved.
487